From 74f411fd407e03f5a5d87e285112fb91b6098049 Mon Sep 17 00:00:00 2001
From: Morgan Adkisson <adkissonmorgan@gmail.com>
Date: Wed, 18 Jan 2023 11:08:48 -0800
Subject: [PATCH] Implements solution for possible_biparition exercise

---
 graphs/possible_bipartition.py | 50 +++++++++++++++++++++++++++++-----
 1 file changed, 43 insertions(+), 7 deletions(-)

diff --git a/graphs/possible_bipartition.py b/graphs/possible_bipartition.py
index ca55677..7f9e744 100644
--- a/graphs/possible_bipartition.py
+++ b/graphs/possible_bipartition.py
@@ -1,12 +1,48 @@
 # Can be used for BFS
-from collections import deque 
+from collections import defaultdict, deque 
 
 def possible_bipartition(dislikes):
-    """ Will return True or False if the given graph
-        can be bipartitioned without neighboring nodes put
-        into the same partition.
-        Time Complexity: ?
-        Space Complexity: ?
+    """ 
+    Will return True or False if the given graph
+    can be bipartitioned without neighboring nodes put
+    into the same partition.
+    Time Complexity: O(N)^2
+    Space Complexity: O(N)
+
+    Example -
+    input: 
+        dislikes = { 
+            "Fido": [],
+            "Nala": ["Cooper", "Spot"],
+            "Cooper": ["Nala", "Bruno"],
+            "Spot": ["Nala"],
+            "Bruno": ["Cooper"]
+            }
+    output: 
+        True
     """
-    pass
+    # 
+    if len(dislikes) == 0:
+        return True
+
+    play_area = {}
+    stack = []
+
+    for dog in dislikes:
+        # assign unassigned dog to play area + add to stack
+        if dog not in play_area: 
+            stack.append(dog)
+            play_area[dog] = 0
+            # look at stack and check neighbors
+            while stack:
+                current = stack.pop()
+                # assign neighbors to group 
+                for neighbor in dislikes[current]:
+                    if neighbor not in play_area:
+                        stack.append(neighbor)
+                        play_area[neighbor] = 1 - play_area[current]
+                    elif play_area[neighbor] == play_area[current]:
+                        return False
+
+    return True